
Open access
Date
2011-10Type
- Journal Article
Abstract
This paper is on developing stochastic analysis simultaneously under a general family of probability measures that are not dominated by a single probability measure. The interest in this question originates from the probabilistic representations of fully nonlinear partial differential equations and applications to mathematical finance. The existing literature relies either on the capacity theory (Denis and Martini), or on the underlying nonlinear partial differential equation (Peng). In both approaches, the resulting theory requires certain smoothness, the so-called quasi-sure continuity, of the corresponding processes and random variables in terms of the underlying canonical process. In this paper, we investigate this question for a larger class of non-smooth" processes, but with a restricted family of non-dominated probability measures. For smooth processes, our approach leads to similar results as in previous literature, provided the restricted family satisfies an additional density property. Show more
Permanent link
https://doi.org/10.3929/ethz-b-000028169Publication status
publishedExternal links
Journal / series
Electronic Journal of ProbabilityVolume
Pages / Article No.
Publisher
Institute of Mathematical StatisticsOrganisational unit
03844 - Soner, Mete (emeritus) / Soner, Mete (emeritus)
More
Show all metadata